Directly opposite the RDS in Dublin, on the site of the former AIB headquarters, stand two impressive new office blocks separated by a plaza, Fibonacci Place.
Leonardo Bonacci – known as Fibonacci, the son of Bonaccio – lived from 1170 to about 1245 AD. It is he who we must thank for bringing us the numeration system that we use every day, that played an essential role in advancing commerce and finance in Europe, and that made our industrial and technological development possible.
Fibonacci hailed from Pisa, but his father had business interests in north Africa, and he was educated in what is today Algeria. There he encountered the Hindu-Arabic numeration system and recognised its great superiority over the Roman numerals then in general use in Europe. Babylonian numbers, with base 60, were awkward. The Hebrew and Greek numerals were denoted by letters of their respective alphabets, with new letters introduced for higher powers of 10. Neither had a means of denoting zero.
The Romans took a giant step backwards: who has not seen a string like MDCCCXLVII on a clock tower and spent half a minute disentangling it. Following the magnificent flowering of mathematics in Classical Greece, the cumbersome Roman numeration system led to stagnation and was a major obstacle to progress. The Romans made many contributions to architecture and engineering but produced not a single new result in mathematics during the 500 years of the Empire.
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The numbers we use today, with 10 decimal digits from 0 to 9, emerged in India sometime around AD 500. Some three centuries later the system was adopted by scholars in the House of Wisdom in Baghdad during the Islamic Golden Age, when texts in science and medicine from ancient Greece, Persia and India were translated into Arabic. Among these scholars was the Persian mathematician Al-Khwarizmi, the founder of algebra. The Indian numeration system became known as the Hindu-Arabic numerals after it was introduced to Europe in the 13th century through translations of the Arabic texts into Latin.
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Fibonacci appreciated the value of the Hindu-Arabic system, with its positional notation, its power to simplify calculations and its vast superiority compared to the Roman numerals used up to that time. In his book Liber Abaci, published in 1202, Fibonacci introduced the system – he called it the “modus Indorum” – with 10 decimal digits, the value of each digit in a number depending on its position. Thus, the first 2 in 1202 signifies two hundred while the second means simply two. The zero enables missing decades to be indicated, removing any ambiguity. Fibonacci demonstrated the great practical value of the method in bookkeeping, commerce and finance.
The word “Abaci” of Fibonacci’s title signifies calculation without the aid of an abacus. A practitioner of these techniques was called an algorist. This name derives from Al-Khwarizmi. The term gradually morphed to algorithm and more recently acquired the significance it holds today, where algorithms play a central role in decision making.
Hindu-Arabic numerals gradually replaced the unwieldy Roman system, greatly aiding the advancement of accounting and banking, and facilitating currency conversions and calculation of interest. They also simplified computation with fractional quantities, later leading to the concept of decimal notation – so simple if only you can remember where to put the dot.
Fibonacci is also remembered for introducing a sequence of numbers that occur unexpectedly in many fields of mathematics and in the natural world; but that is another story.
Peter Lynch is emeritus professor at the School of Mathematics and Statistics, University College Dublin. He blogs at thatsmaths.com
